Tuchel, appointed boss on Tuesday following the sacking of Frank Lampard, took his place in the dugout after conducting one training session with his new team.
But the German was given an indication of the huge challenge facing him as Chelsea struggled to carve out chances against a Wolves side short of confidence and without a top-flight win since 15 December.
Rui Patricio produced good saves to keep out Antonio Rudiger’s header and Callum Hudson-Odoi’s deflected attempt, while Chelsea’s 433 successful passes were the most by a Tuchel team in the first half of a top-flight game since May 2016.
Ben Chilwell sent a rare chance over the bar but Wolves, who hit the bar through Pedro Neto and gave a debut to striker Willian Jose, were good value for their point.
When Lampard took charge of his first league match at Stamford Bridge in August 2019 – a 1-1 draw with Leicester – fans unfurled a ‘Welcome Home Super Frank’ banner.
With no supporters allowed inside the ground because of the coronavirus pandemic, there was no such fanfare for Tuchel, who went straight to his seat in the dugout when he appeared from the tunnel dressed in a blue club coat.
Reminders of the previous regime were evident inside Stamford Bridge.
A ‘Super Frankie Lampard’ banner remained on display but the arrival of a new boss inevitably heralded change and England trio Mason Mount, Reece James and Tammy Abraham, who had made 39 Premier League starts between them under Lampard this season, started on the bench.
Tuchel was animated throughout, the German at one stage throwing his arms in the air after Hudson-Odoi clipped a cross to the back post only for Chilwell to put it wide.
He repeated the gesture in the second half when Chilwell fired another chance over the bar and Mateo Kovacic went close from long distance.
Former Borussia Dortmund and Paris St-Germain boss Tuchel will demand more urgency from his players, who were pedestrian for spells.
Having conceded 77 goals in 57 Premier League games under Lampard, Chelsea will take some comfort in a clean sheet.
But Tuchel knows he has to get expensive signings like Timo Werner and Kai Havertz firing – and Chelsea winning.
Wolves are without a Premier League win in seven games but they dug deep to take a valuable point back to the Black Country – despite failing to register an attempt on target.
Nuno Espirito Santo’s side have endured a torrid time since beating Chelsea, thanks to Neto’s 95th-minute winner, at Molineux on 15 December.
They arrived in London having picked up just two points from a possible 18.
Yet they stifled Chelsea for spells on their way to a first top-flight clean sheet since 30 October.
Wolves have struggled since losing Raul Jimenez to serious injury but Nuno will hope the arrival of new loan signing Jose, who has scored 62 goals in 170 appearances for Real Sociedad – as well as the return of Daniel Podence from injury – will push his team on after an awkward spell of results.
They went close to securing all three points when Neto lifted the ball beyond Edouard Mendy, the Portugal winger’s attempt landing on top of the bar.